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On interval routing schemes and treewidth. (English) Zbl 0892.68069
Summary: We investigate which processor networks allow \(k\)-label interval routing schemes, under the assumption that costs of edges may vary. We show that for each fixed \(k\geq 1\), the class of graphs allowing such routing schemes is closed under minor-taking in the domain of connected graphs, and hence has a linear time recognition algorithm. This result connects the theory of compact routing with the theory of graph minors and treewidth. We show that every graph that does not contain as a minor has treewidth at most \(2r- 2\). As a consequence, graphs that allow \(k\)-label interval routing schemes under dynamic cost edges have treewidth at most \(4k\). Similar results are shown for other types of interval routing schemes.

MSC:
68R10 Graph theory (including graph drawing) in computer science
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